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The problem asks us to write the given system of equations in augmented matrix form. Let's analyze the equations:

1. \( c - 3m = 300 \)
2. \( 3c - 11m + b = 150 \)
3. \( -3m + b = 400 \)

### Step-by-Step Solution:

To create the augmented matrix:
1. Arrange the equations in standard form: coefficients of \(c\), \(m\), and \(b\) (if present) on the left-hand side, with constants on the right-hand side.
2. Use the coefficients of the variables as matrix entries, including zeros for missing variables.
3. Place the constants on the right-hand side as the last column.

#### Standardized Equations:
- Equation 1: \( c - 3m + 0b = 300 \) → Coefficients: \([1, -3, 0 | 300]\)
- Equation 2: \( 3c - 11m + b = 150 \) → Coefficients: \([3, -11, 1 | 150]\)
- Equation 3: \( 0c - 3m + b = 400 \) → Coefficients: \([0, -3, 1 | 400]\)

#### Augmented Matrix:
\[
\begin{bmatrix}
1 & -3 & 0 & 300 \\
3 & -11 & 1 & 150 \\
0 & -3 & 1 & 400
\end{bmatrix}
\]

### Final Answer:
The augmented matrix for this system is:
\[
\boxed{
\begin{bmatrix}
1 & -3 & 0 & 300 \\
3 & -11 & 1 & 150 \\
0 & -3 & 1 & 400
\end{bmatrix}
}
\]

Would you like me to explain further or assist with solving the system of equations?  

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### Related Questions:
1. What is the purpose of augmented matrices in solving linear systems?
2. How can this matrix be solved using row-reduction (Gaussian elimination)?
3. What are other methods for solving this system besides matrices (e.g., substitution)?
4. How would you interpret the solution geometrically if \(c\), \(m\), and \(b\) represent variables in 3D space?
5. How can software like MATLAB or Python help solve such matrix problems?

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### Tip:
When creating an augmented matrix, always ensure the variables are ordered consistently across all equations!

Write the system of equations as an augmented matrix.

Understand how to write a system of linear equations as an augmented matrix. This solution covers the concepts of matrix representation and standardizing equations, suitable for high school and early college students.

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